Q: How do I find the love of my life? (a Mathematician’s perspective)

Mathematician: The Physicist and I were once asked “how do I find the love of my life?”. Never ones to shy away from applying math to love (or anything else), the Physicist gave his take on this question (noting the connections between finding a mate and the famous “secretary problem”), and here I am, taking a stab at love from a different angle, tackling the problem using math and logic in the hope of producing useful advice.

It’s important to note that the question itself is deeply ambiguous. Part of the reason that math is so powerful is because it relies on applying deduction to precise definitions, so when mathematicians get answers, pretty much everyone who understands them can agree they are correct. Even for the insanely complex and specialized proof of the Poincaré conjecture, a consensus about its correctness was reached in just a few years (a short time by the standards of other fields). Hence, in the spirit of mathematical proof, we proceed by trying to formalize our question by developing a precise definition.

Let the “love of your life” be the currently living person who (if you got to know them) would:

1. Fall romantically in love with you for as long as he or she lives.
2. Cause you to fall romantically in love with her or him for as long as you live.
3. Increase your average happiness at least as much as any other person satisfying both (1.) and (2.), if you were to become life partners.

Unfortunately, due to the limitations of the English language, and  a notable lack of happiness measuring devices, we will be forced to sweep under the rug sticky issues such as:

• how, precisely, to define “romantic love”
• what exactly is meant by “happiness” (e.g. how do we compare the happiness generated by a good shoulder rub with the happiness caused by a great conversation? The appropriate conversion rate between different types of happiness, if such a rate even makes sense to talk about, is very problematic to define)
• whether there could be more than one “love of your life” for a given person (my answer: with high probability each person only has one, due to the fact that our definition involves the person who makes you happiest, and total happiness over a long stretch of time can take on a huge variety of distinct numerical values, so it’s unlikely that the two best people for you give you precisely the same value).

In any event, I am sad to report that when applying the above definition for “the love of your life”, finding “the one” is essentially impossible. I strongly urge you not to try it. The probability that you meet the single person that would make you happiest of all is extremely small. There are about 7 billion people on earth, and (let’s say) more than a billion within a reasonable dating age range of you. That implies that there are at least 500 million people of the appropriate gender (a bit more if you are bisexual). Even if it is the case that you are rather narrow minded, and just 1 in 200 people are culturally similar enough to you for you to even consider a romantic relationship (e.g. you are a Baptist American, who would only ever be willing to date another Baptist American), that still leaves at least 2.5 million people to search through. To meet just half of those people (and therefore have anywhere close to a 50% chance of meeting the “love of your life”) you would have to be meeting, on average, more than 40 potential mates each day over a period of 80 years.

In practice, maybe you could do a bit better by being selective about who you meet (for example, concentrating your efforts on those places where you would suspect “the one” would hang out). But even so, you’re (non-literally) screwed, as the odds of meeting this person are negligible. In fact, the only way that you could have a decent chance of meeting that person is if you had such stringent dating criteria that you would be unhappy with anyone that fell outside of a small, easy to locate group. Unfortunately, while this strategy is great for maximizing the chances of finding the “love of your life”, it is terrible for maximizing your happiness (official mathematician advice: don’t go join a cult where you are not permitted to date non-cult members, on punishment of eternal damnation).

So if trying to find the “love of your life” is a bad idea, what should a person do? Well, when mathematicians don’t like what they can derive from one starting point, they often can just alter their problem or definitions a little (you should feel bad for those poor physicists who are limited by what actually exists. We mathematicians frolic in the realm of pure ideas!).

Looking for love shouldn’t be about finding the best person. As we’ve seen, that is usually close to impossible, and even when possible, a bad idea. It is much smarter to view the search for love as an attempt to maximize your total lifetime romantic happiness over the rest of your life. This viewpoint leads to a very different optimal strategy than one would use to try to find the single best person. The total romantic happiness maximizing approach implies working to increase the moment to moment satisfaction you feel due to your romantic life, added up (or if time is continuous, integrated) over all of your remaining moments.

From now on, we will refer to a person employing such a romantic happiness maximizing strategy as a “Romaximizer”, and will kick the mathematics into high gear, introducing the Romaximizer equation:

$\large{ \displaystyle{ \large{ \bf{ \textrm{Total Romantic Happiness} \approx \frac{L H}{\frac{1}{T P F D M} + 1}}}}}$

where

• L is the number of years you have left to live
• H is the average amount of happiness per relationship year (that is, per year of time spent in relationships) that you will derive from your future relationships
• T is the average number of years that you will spend in each future relationship
• P is the average number of new people that you will meet per year
• F is the fraction of the people that you will meet that you will find sufficiently physically and personally attractive to consider dating
• D is the fraction of those people you will want a relationship with who will actually be willing to have a relationship with you
• M is the fraction of those people that you will find sufficiently attractive to consider dating that you will decide to try to actually begin a romantic relationship with

The Romaximizer equation is only an approximation, and hence the reason the equation uses  “$\approx$” rather than “$=$“, but it should be plenty accurate for our purposes (for those interested, I’ve included the proof of the equation at the bottom of this article). An important thing to note about it is that increasing the value of any one of the variables will increase Total Romantic Happiness, so long as all of the other variables are simultaneously left unchanged. Hence, all else being equal, L, H, T, P, F, D and M are things that we should try to increase (though as we’ll see, some of them involve tradeoffs where increasing one variable decreases another). This formula leads us directly to a variety of specific strategies for improving our total romantic happiness, which I will now discuss in detail.

1. Increase L, the number of years you have left to live. It is of course the case that the longer you live, the more potential time for romantic companionship you will have. Dying young is an especially bad strategy for the Romaximizer. Fortunately, there are plenty of simple (though not necessarily easy) things we can do to promote long life. According to government statistics, out of all deaths in the United States in 2007, about 25% were caused by diseases of the heart (staying within a healthy weight range, exercising, and not smoking cigarettes is believed to reduce this risk), 23% were caused by malignant cancerous tumors (maintaining a healthy weight, avoiding cigarettes, and avoiding excessive drinking are believed to help), 5.6% were attributable to cerebrovascular diseases which can lead to strokes (high blood pressure is a culprit, and smoking and obesity appear to be risk factors), 5.3% were caused by chronic lower respiratory diseases (you guessed it, smoking is implicated yet again), 5.1% were due to accidents (an easy way to reduce this risk is to always wear your seatbelt, since if you break it down further, about 1.5% of deaths are due to car accidents), 2.2% were due to Influenza or Pneumonia (remember to get your flu shot if you’re a member of an at risk group), and 1.4% were due to suicide (if you feel depressed on a regular basis, get yourself to a CBT therapist or psychiatrist right away, before it gets any worse). With health, there will always be luck involved, but there fortunately are a number of steps we can take to significantly improve our odds.
2. Increase H, the average amount of romantic happiness per year spent in future relationships. One simple approach to raising this variable is to increase your pickiness with respect to those traits that really make a big difference to your happiness in a relationship. So long as your beliefs about what in a mate makes you sustainably happy are fairly accurate, greater selectivity should increase the average quality of your relationships. Unfortunately, there is a tradeoff here, as this will decrease M, the fraction of people who you are attracted to that you ultimately decide to enter into a relationship with (and as we know, decreasing any of our variables tends to reduce total romantic happiness). We get a simple rule of thumb for deciding whether increasing H is worth the amount you’d have to decrease M by noting that when the product of variables T P F D M is significantly bigger than 1 (which basically means that you get into relationships easily with little gap between them and they last for a substantial time), then the Romaximizer equation simplifies to $\textrm{Total Romantic Happiness} \approx L H$ (a value of more than 6 for T P F D M will make the approximation accurate to within about 15%). That means that under those conditions, if you can increase H by becoming more picky (i.e. by decreasing M) then you should do so since there is little cost as seen in the simplification of the equation. There are other strategies for increasing H, of course. For instance, if you have had a number of relationships in the past, you could try making a list of problems that arose in them, and a corresponding list of things that you could have done to help prevent or fix those problems. Review these strategies a few times before getting into a new relationship, so that you are primed to use them the next time around!
3. Increase T, the average number of years that you spend in each romantic relationship. Like H, the variable T can be increased by being more picky about who you enter into a relationship with (i.e. by decreasing M). The Romaximizer equation immediately shows us the tradeoff between T and M: as long as we are increasing the product T M, our total romantic happiness will be improving. That means that if you think you can increase the average length of your relationships by 40% by being 20% more selective regarding who you start a relationship with (so causing T to increase by the multiple 1.4 causes M to decrease by the multiple 1-0.2 = 0.8), then the product T M will increase by 1.4*0.8 = 1.12 > 1, so your total romantic happiness will be improved. It’s worth noting that often H and T come into conflict. When your happiness is falling in a relationship, you have the choice of increasing T (staying, even though you aren’t so happy), or trying to find someone else who will make H larger. The right choice for increasing total net happiness is going to depend on how difficult it is for you to find someone else that will make you happier than your current partner. For example, consider a case where your happiness in the relationship has waned substantially, and you have truly exhausted strategies for improving it (and there aren’t religious or children related reasons to stay together). If finding another person who makes you happier is unlikely to take you very long, then a breakup is likely a romantic happiness maximizing strategy.
5. Increase F, the fraction of the people that you meet that you find sufficiently physically and personally attractive to consider dating. While we may not have a great deal of control over who we find attractive, there are still a variety of things we can do to try to increase F. (i) How likely you are to be attracted to a person you meet is going to depend on where you meet that person. Not every place to meet a person is equally good. For example, an intellectual snob shouldn’t be picking up men at WWE matches (not that there is anything wrong with men in spandex pretending to hurt each other), and the wicked witch of the west shouldn’t be meeting people at pool parties. The main things to consider are, “how many people am I likely to meet at place X?” and, “what’s the probability that each person I meet at place X will be someone I have a mutual romantic attraction with?” Maximizing romantic happiness isn’t just about meeting a lot of people, but also about meeting them at places where you are more likely to find people that you like. (ii) The physical attractiveness we feel for a person can rise over time as we get used to them, especially if we appreciate his or her personality a lot. So if we meet someone who we don’t quite think meets our physical attractiveness threshold, but who we like a lot and think we would be compatible with, it may well be worth it to get to know them better and explore whether physical attraction could develop (e.g. by becoming friends). Eliminating someone because you don’t find them super good looking on the first date may not be a winning strategy overall. (iii) Sometimes our ideas of who we find attractive and who we think we should find attractive can get somewhat mixed up. If you think that social pressure of some kind is affecting how attracted you are to someone (e.g. your friends don’t think she’s hot, or he’s not part of the cool crowd), then ask yourself how much happiness you are likely to get from pursuing this person, versus how much unhappiness you are likely to have due to violating the social pressure. Another thought experiment that can be fruitful is to ask yourself how much you would enjoy being with the person if nobody else’s opinion mattered and nobody else cared. (iv) Sometimes we make rules for who we consider ourselves to be compatible with that don’t actually have much bearing on what really matters. People will have a list of traits that they feel a person must (or must not) have in order to be boyfriend/girlfriend/spouse worthy. The appropriate question to ask yourself is: “If a person lacks (or has) this trait, how much will it affect my happiness with them overall?” If the answer is “only a small amount”, it should probably be taken off the deal breaker list. By lowering your standards in the less important areas, you can afford to raise them in the more important ones (i.e. those that will more substantially affect your happiness).

In conclusion, you do have the power to increase your expected total romantic happiness. It is up to you to take steps to live longer, become more selective about who you enter in a relationship with when lots of dating options are available, avoid forming attachments before you know a person well, increase your options by making an effort to meet people (much) more frequently than you are currently meeting them, hang out at places where people you like are more likely to be found, adjust your standards so that you aren’t eliminating dating partners based on criteria that don’t have much bearing on your likely future happiness with them, recognize that attraction can build over time, make that extra effort to talk to every attractive person at each event you go to, and take steps to become more attractive to others.

Derivation of the Romaximizer Equation

This entry was posted in -- By the Mathematician, Biology, Equations, Philosophical, Probability. Bookmark the permalink.

21 Responses to Q: How do I find the love of my life? (a Mathematician’s perspective)

1. Aaron Davies says:

there’s an implicit “1” somewhere in the romaximizer that hides another way to increase TRH. does anyone care to generalize it to handle polyamory?

2. The Mathematician says:

Yes, you are absolutely right, the Romaximizer equation assumes monogamy (since the majority of adults in English speaking countries are primarily monogamous, this seemed like a reasonable assumption). Many of the strategies mentioned also apply to polyamory (though not all of them).

3. Boris says:

Geez, there weren’t any posts from The Mathematician for quite a while. Were you all this time off, working on this voluminous post?

4. The Mathematician says:

Yeah, pretty much!

5. Ari says:

If the whole mathematician thing doesn’t work out, there’s surely a job waiting for you at OkCupid.

6. Joel says:

Its seems these are ways to maximize finding the love of your life but how do you know when you’ve found them? How does well does selecting a candidate correlate with the likelihood for long term happiness? You need to know what factors support long term happiness and the early behavioral indicators to be observed in the beloved. Falling in love with someone may be a necessary condition of their being the love of your life but the rate of false positives is too high to be considered a reliable heuristic. The marker or romantic love, falling madly in love may sometimes or often or usually be a confounding factor by its tendency to cloud reason.

7. Johann Fuchs says:

i see a few differential equations popping out up there, which would simplify the whole equation quite a lot

8. Tim Anderson says:

This answer assumes that you want to maximize total romantic happiness and it doesn’t consider other types of happiness that can be affected by the romances. Or is that taken into account by adjusting H? Increasing the amount of your time in relationships only increases happiness as long as H is positive. If H is negative, your best bet would be to stay away from romance until you can increase H. Decreasing L would also work to increase total lifetime happiness.

9. mehnaz says:

how to our real life love

10. julz julia says:

Daaaaaammmmmmmmmmnnnnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!! the mathematician is super calculative!!!!!!!!!!!!!! such math will do lovers to be pretty much!

11. Ron says:

The probability of finding true love precisely equals 0^0. lol

12. Tam says:

Love is complicated…

13. Pamela Cain says:

There has only ever been one love of my life and it is infinite. The certainty of my love resides in that place in my being where I experience our oneness. are we in this love in two separate places in time? It can’t be because he/she is here with me now in pure energertic form somehow. Who is it? I only know to say “my love” and feel our closeness. Is my love from another planet and can somehow see me at all times and send the waves to me which seem to transform to particals of a thing I cannot define? Out there and in here all at the same time for eternity.

14. Alexis says:

It’s unfortunate that I am unable to experience my romantic moments cumulatively.

15. Diana says:

I am a mathematician and have fallen in love with your explanation <3…Love your website too, cheers!

16. looking for an answer says:

17. Medhavi Mishra says:

I have met this person, who likes me..I like him…but we have future goals..
I want to be an astrophysicist and he wants to become a nuclear physicist.
We don;t want any relationship. But we talk like, “we will meet 10 years later”
So I wanted to know what is the probability that we will meet and how do I calculate it.
We have just passed High school with A1 grade. (highest of all in my country)

18. Armanda says:

That’s why my idealist self doesn’t apply mathematics to love. The approach here is good for filling in the time till the best finds you but not as a final aim. Maximize all you want but… all the happiness years achieved according to this equation won’t measure up to a single moment passed with your best. I don’t want one big blur of mediocre romance and say, “gee, look how many years of this stuff I’ve had.” Settling temporarily – sometimes we need to rest at a nice spot – is alright. But if you have to settle long term for something/someone that you don’t know and feel is your best, you might as well have died.

Don’t go nuts looking for it. Let it find you. But, by all means, stay open for your best. When it finds you, it’s going to blow not only mathematics but everything you (thought you) knew out of the water.

The best that can’t / won’t be topped is the one that you’ll remember, not the blur. It’s about quality too, not just quantity, sorry mathematics. This is not a this-tin-is-my-life-let’s-calculate-the-max-number-of-sardines-I-can-fit-in-it problem. The BEST tasting sardine in my tin only 1% of the time is still more worth experiencing than a lifetime supply of sardines.

Clearly, mathematician wrote this BB (Before Best)